2 CHAPTER 1 Advanced Euclidean Geometry
to Euclidean geometry. President James Garfield published a novel
proof in 1876 of the Pythagorean theorem (see Exercise 3 on page 4).
As for the subject itself, it is my personal feeling that the logical
arguments which connect the various theorems of geometry are every
bit as fascinating as the theorems themselves!
So let’s get on with it ...!1.2 Triangle Geometry
1.2.1 Basic notations
We shall gather together a few notational conventions and be reminded
of a few simple results. Some of the notation is as follows:
A, B, C labels of points
[AB] The line segment joining AandB
AB The length of the segment [AB]
(AB) The line containingAandB
 The angle atACAB̂ The angle between [CA] and [AB]
4 ABC The triangle with vertices A, B, andC
4 ABC∼= 4 A′B′C′ The triangles 4 ABC and 4 A′B′C′are congruent
4 ABC∼4A′B′C′ The triangles 4 ABC and 4 A′B′C′are similar